We study the transport properties of a quasi-two-dimensional diffusive
normal metal film attached to a superconductor. We demonstrate that t
he properties of such films can essentially differ from those of quasi
-one-dimensional systems: In the presence of the proximity-induced sup
erconductivity in a sufficiently wide film, its conductance may not on
ly increase but also decrease with temperature. We develop a quantitat
ive theory and discuss the physical nature of this effect. Our theory
provides a natural explanation for recent experimental findings referr
ed to as the ''anomalous proximity effect.''